Thermodynamics Relations - Proof 5

For the Vander Waals gas

From Equn.3.4,

   à (5.1)

For the Vander Waals gas,

i.e.,

   à (5.2)

differentiating with respect to T at constant V,

   à (5.3)

Substituting from Equn.5.3 in Equn.5.1,

   à (5.4)